The Harmonic Language of György Ligeti

 

!"# %&'()*+, -&*./&.# ): 714'.1 -+.#5+ Unc ackmbbmbk f` tnc 1:tn Dcbtury sgw wmecsprcge sfdmgl, pflmtmdgl, tcdnbflfkmdgl gbe grtmstmd dngbkc. G emvcrsmty f` ousmdgl kcbrcs cxplfece mbtf cxmstcbdc, mbdluembk bcw trgemtmfbs sudn 7

gs igzz, rfdh, rgp, `mlo ousmd gbe ftncr pfpulgr stylcs.  Aurhnflecr ct gl emsduss g smomlgr splmbtcrmbk f` tnc dlgssmdgl trgemtmfb mbtf buocrfus bcw emrcdtmfbs, mb pgrtmdulgr tnc cgrly 1:tn  Dcbtury „ofecrbmst” ofvcocbt tngt rcicdtce tnc ousmdgl trgemtmfbs f` tnc pgst.1 Fbc f` tnc ofst mopfrtgbt gspcdts f` ofecrbmso wgs tnc scgrdn `fr bcw ngrofbmd lgbkugkcs. Pmbdcbt Zcrsmdncttm mecbtm`mcs tnms gs g ofvcocbt gwgy `rfo tfbglmty, gbe tnc ecvclfpocbt f` `rcc gtfbglmty, scrmglmso gbe pflytfbglmty gofbk tcdnbmqucs. 4 Ofecrbmso mtscl` wgs lgrkcly rcicdtce ay g yfubkcr kcbcrgtmfb f` dfopfscrs `rfo tnc 7=3:s fbwgres, wnf drcgtce g bcw trcbe f` „pfstofecrbmso.” Gltnfukn tnc emvcrsmty f` pfstofecrb ousmd ms em``mdult tf rceudc tf smbkulgr stylcs, Igbb Zgslcr mecbtm`mcs tnrcc ogifr trcbes9 g „pfstofecrbmso f` rcgdtmfb” (Bcf-rfogbtmdmso), g „pfstofecrbmso f` rcsmstgbdc” (Ombmoglmso) gbe g „pfstofecrbmso f` cdlcdtmdmso” (ousmd wmtn cdlcdtmd mb`lucbdcs, pgrtmdulgrly tngt f` `frcmkb dulturcs). Mb kcbcrgl, tncsc tnrcc strgbes f` pfstofecrbmso rcicdtce gtfbglmty gbe arfuknt gspcdts f` tfbgl ngrofby mbtf g ofecrb dfbtcxt. Bcf-rfogbtmdmso rcbcwce mbtcrcst mb tnc ngrofbmd, oclfemd gbe tn tn strudturgl prgdtmdcs dngrgdtcrmstmd f` 7>  gbe 7=  Dcbturmcs, Ombmoglmso mbtrfeudce g rgemdglly smoplm`mce tfbgl lgbkugkc, gbe cdlcdtmd pfstofecrbmst stylcs dfoambce tnc [cstcrb tfbgl trgemtmfb wmtn tnc ngrofbmd prgdtmdcs f` `frcmkb dulturcs.5 Ogby dfopfscrs emeb”t suasdrmac tf g smbklc stylmstmd trcbe nfwcvcr, aut `froce tncmr fwb ngrofbmd stylc tngt cvflvce wmtn tnc dngbkmbk trcbes gdrfss tnc 1: tn Dcbtury.3 Unms cssgy wmll mbvcstmkgtc tnc cvflutmfb f` Nubkgrmgb dfopfscr Kyðrky Lmkctm”s ngrofbmd lgbkugkc8 `rfo tfbglmty tf gtfbglmty gbe tncb tf g qugsm-tfbgl dfoambgtmfb f` tnc twf. 0  Uf dfbtcxtuglmsc oy rcscgrdn f` Lmkctm, M rc`crrce tf lmtcrgturc fb tnc arfgecr suaicdts f` ofecrbmso, pfstofecrbmso gbe 1:tn Dcbtury ngrofby mb dfbtcopfrgry dlgssmdgl ousmd. Mb  pgrtmdulgr, M wgs mb`froce ay Ousmd mb tnc Uwcbtmctn gbe Uwcbty-@mrst Dcbturmcs ay Ifscpn Gubcr, G Nmstfry f` [cstcrb Ousmd ay Aurhnflecr ct gl, Pmbdcbt Zcrsmdncttm”s Uwcbtmctndcbtury Ngrofby9 Drcgtmvc Gspcdts gbe Zrgdtmdc gbe Igbb Zgslcr”s Krfvc Ousmd Fblmbc grtmdlc Zfstofecrbmso. @fr oy amfkrgpnmdgl ubecrstgbembk f` Lmkctm, M dfbsultce tnc Krfvc

7

Uwcbtmctn tn gbe Uw Uwcbty-@mrst cbty-@mrst Dcbturmcs (Bcw ]frh, Sbmtce Ttgtcs9 [[  Ifscpn Gubcr,  Ousmd mb tnc Uwcbtmc  Bfrtfb & Df, D f, 1:74). 1 [cstcrb rb Ousmd , ce.  I. Zctcr Aurhnflecr, Efbgle Igy Krfut, gbe Dlguec v. Zglmsdg,  G Nmstfry f` [cstc Ogrmactn Zgybc, > ce. (Lfbefb  Bcw ]frh9 ]frh 9 [.[. Bfrtfb & Dfopgby, Mbd., 1:7:). 1: 7:). 4  Pmbdcbt Zcrsmdncttm, Uwcbtmctn-Dcbt Uwcbtmctn-Dcbtury ury Ngrofby9 Drcgtmvc Gspcdts gbe Zrgdtmdc, Mllustrgtce Cemtmfb ce. (Bcw ]frh9 [.[. Bfrtfb & Df. Mbd., 7=07). 5  Igbb Zgslcr,  Zfstofecr  Zfstofecrbmso bmso (Krfvc Ousmd Fblmbc9 Fx`fre Sbmvcrsmty Zrcss, 1::7). 3  Aurhnflecr, Krfut, gbe Zglmsdg. 0  Omhc Tcgray, "Lmkctm tnc Zfstofecrbmst6," Ucopf, bf. 7== (7==;), nttps9//www.istfr.frk/stgalc/=533136scq?7.  

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 Ousmd Fblmbc amfkrgpny ay Zgul Krm``mtns gbe oy gbglysms f` Lmkctm”s ngrofbmd lgbkugkc wgs mb`froce tnrfukn stueymbk ifurbgl grtmdlcs gbe affhs fb tnc suaicdt ay Ogyvmllc, Erftt, Tcgray, Qfmk-@rgbdflm gbe Ugylfr, gbe mb wgtdnmbk/lmstcbmbk tf sdfrc vmecfs fb ]futuac (nms sdfrcs grcb”t mb tnc pualmd efogmb). Fbc f` tnc ofst mopfrtgbt sfurdcs tf mb`fro tnms pgpcr wgs Zítcr Pçrbgm”s affh Lmkctm mb Dfbvcrsgtmfb, wnmdn wgs g prmogry sfurdc tngt wgs  pgrtmdulgrly nclp`ul tf ubecrstgbe Lmkctm”s fwb tnfuknts fb nms nms stylc.  Lmkctm”s ousmdgl ackmbbmbks wcrc mb Nubkgry, wncrc nc stuemce gbe tguknt gt tnc Hflfzsvgr Dfbscrvgtfry actwccb 7=57 gbe 7=30. Euc tf gb fpprcssmvc dfooubmst kfvcrbocbt, nc wgs dfbstrgmbce tf wrmtmbk bgtmfbglmst ousmd mb g trgemtmfbgl tfbgl stylc gbe wgsb”t cxpfsce tf tnc bcw ousmdgl ecvclfpocbts fddurrmbk mb tnc [cst. [mtn tnc Nubkgrmgb rcvflutmfb f` 7=30 gbe mts vmflcbt supprcssmfb ay tnc Tfvmct Groy, Lmkctm `lce tf Pmcbbg gbe tncb Dflfkbc, wncrc nc wgs eccply mb`lucbdce ay tnc cxpcrmocbtgl clcdtrfbmd wfrhs f` Ttfdhnguscb gbe Hgkcl gbe ftncr dfbtcopfrgry grt ousmd. Unrfukn tnms bcw cxpfsurc tf tnc gvgbt kgrec, Lmkctm ecvclfpce g `rcsn dfopfsmtmfbgl stylc `fr nmoscl`. Unms dfbsmstce f` gb glofst dfoplctc rclmbqumsnocbt f` dfbvcbtmfbgl bftmfbs f` ngrofby, oclfey gbe rnytno, tnrfukn tnc  iuxtgpfsmtmfb f` ecbsc sfube alfdhs tngt cbkcbecr cbkcbecr g `fdus fb tcxturc gbe tmoarc. Unms stylc ms  prcscbt mb nms cgrly pmcdc Gtofspncrcs, wnmdn kgmbce Lmkctm smkbm`mdgbt gttcbtmfb mb tnc grt ; ousmd dfooubmty `fllfwmbk mts prcomcrc gt tnc 7=0: MTDO `cstmvgl mb Dflfkbc.  Lmkctm ecvclfpce upfb tnc gtfbgl „sfube ogss” tcdnbmquc f` cgrlmcr dfopfscrs sudn gs Mvcs gbe Dfwcll mb tnms pmcdc, wncrc tnc “mbemvmeugl mbtcrwfvcb mbstruocbtgl vfmdcs grc gasfrace mbtf > tnc kcbcrgl tcxturc gbe lfsc tncmr mecbtmty.‟  Nc utmlmsce tfbc dlustcrs tf drcgtc g ngrofbmd goamkumty, wncrc ecbsmty ms ofrc mopfrtgbt tf tnc ngrofby tngb mts dfbstmtucbt pmtdncs. Geemtmfbglly, nc mbvcbtce g bcw tcdnbmquc nc dgllce „omdrfpflypnfby”, wncrc cgdn vfmdc smoultgbcfusly plgys tnc pmtdncs f` tnc dlustcr aut wmtn g dfbtrgstmbk rnytno. Unc „omdrf” gspcdt f` tnc tcro rc`crs tf tnc snccr buoacr f` mbemvmeugl vfmdcs tngt Lmkctm ectgmls mb tnc sdfrc (mb dfbtrgst tf dfbvcbtmfbgl pflypnfbmd tcxturcs), wmtn sfoc scdtmfbs f`  Gtofspncrcs dfoprmsmbk f` dfbtrgstmbk lmbcs `fr cvcry plgycr mb tnc frdncstrg. Uncsc mbemvmeugl lmbcs  prfeudc g snmoocrmbk tcxturc tngt drcgtcs tnc ecbsc dnrfogtmd sfube ogss dlustcrs, wnmdn grc `mroly gtfbgl tnrfukn tncmr lgdh f` dfbvcbtmfbgl ngrofbmd `ubdtmfb. =  Lmkctm”s wfrhs Lux Gctcrbg (7=00) gbe Lfbtgbf (7=0;) snfw g `urtncr cvflutmfb f` nms gtfbgl ngrofbmd lgbkugkc. Nc stmll coplfyce dlustcr sfbfrmtmcs gbe omdrfpflypnfby, aut tnc oclfemdmso f` tnc pgrts wmtnmb nms omdrfpflypnfby ms oudn ofrc gppgrcbt gs tnc dlustcrs grc lcss ecbsc. Unms dguscs tnc ousmd tf acdfoc ofrc ngrofbmdglly `fdussce gbe lcss gafut tnc  iuxtgpfsmtmfb f` arfge stgtmd alfdhs f` sfube tngt `fdus fb tcxturc gbe tmoarc. Unc vcrtmdgl sfbfrmtmcs grc oudn ofrc gurglly mecbtm`mgalc gbe tncrc`frc ngvc krcgtcr `ubdtmfb ngrofbmdglly gbe tnc vfmdclcgembk acdfocs ofrc mopfrtgbt tff. Gltnfukn bft `ubdtmfbgl mb g ;

 Zgul Krm``mtns, Lmkctm, Kyðrky K yðrky  (Krfvc Ousmd Fblmbc9 Fx`fre Sbmvcrsmty Zrcss, 1::7).

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 Gubcr. 

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 Ttcpngbmc Ogyvmllc, "Unc Dfopfsmtmfbgl Ucdnbmqucs gbe Mb`lucbdcs Acnmbe Lmkctm”s „Gtofstpnírcs”," Mbtcroczz  Mbtcroczzff 7 (1:73), nttps9//ufttgwg.sdnflgrspfrtgl.mb`f/fttgwg/mbecx.pnp/mbtcroczzf/grtmdlc/vmcw/74>5.

 

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tfbgl scbsc, Lmkctm coplfys stcpwmsc vfmdclcgembk gbe vgrmce ecbsmtmcs tf drcgtc mbtcrvgllmd tcbsmfb gbe rclcgsc. Unc ngrofby ms glsf tnc ogmb ecvmdc f` `frogl ecvclfpocbt wmtnmb tnc  pmcdcs, wncrc tnc fvcrgll sfube tngt tnc omdrfpflypnfby drcgtcs ms tnc krgeugl cvflutmfb f` gb cvcr-cxpgbembk gbe dfbtrgdtmbk dlustcr. Aftn pmcdcs ackmb wmtn g smbklc pmtdn tngt acdfocs twf pmtdncs, tncb `fur gbe dfbtmbucs mb g prfdcss f` cxpgbsmfb gbe dfbtrgdtmfb ofrpnmbk  actwccb vgrmfus vcrtmdgl ngrofbmcs `fr tnc cbtmrc pmcdc.7: 

77

@mk. 79 Gbglysms f` cxpgbembk dlustcr mb  Lux Gctcrbg.  

Mb nms lgtcr wfrhs, Lmkctm `frkce nms fwb pgtn ay arcghmbk `rfo tnc gvgbt kgrec aut glsf bft dfoplctcly `fllfwmbk pfst-ofecrb trcbes9 “M efb”t wgbt tf rcturb tf tnc 7= tn dcbtury, aut M”o bf lfbkcr mbtcrcstce mb sudn dgtckfrmcs gs gvgbt kgrec, ofecrbmso fr gtfbglmty…M ngtc bcfCxprcssmfbmso gbe M dgb”t stgbe tnc bcf-Ognlcrmtc gbe bcf-Acrkmgb g``cdtgtmfbs, iust gs M 71 dgb”t stgbe pfst-ofecrb grdnmtcdturc.‟  Gs pgrt f` tnms stylmstmd snm`t, Lmkctm `froce g qugsmtfbgl ngrofbmd lgbkugkc tngt coplfys gspcdts f` tfbglmty aut tnc “vfdgaulgry…bft tnc sybtgx  74 f` tfbgl ousmd‟.  Unms rc`crs tf tnc usc f` tcrtmgb sfbfrmtmcs wmtnfut trgemtmfbgl tfbgl moplmdgtmfb, glfbksmec gtfbgl pmtdn dlgss scts. Ugylfr suoogrmscs tnc ngrofbmd prgdtmdcs f` Lmkctm”s lgtcr ousmd gs9 7.  Urmges, ogifr fr ombfr mb `mrst mbvcrsmfb8 1.  „fpcb-`m`tn `mcles”, tnfukn bft glwgys grrgbkce vcrtmdglly mb `m`tns8 4.  :, 7, 0 wnmdn dfoambcs trmtfbcs, ogifr scvcbtns, gbe `m`tns — glsf clgafrgtmfbs f` tnms sct sudn gs :,7,1,; fr :,7,4,0,; fr g ogifr trmge wmtn gb geece #`frtn9 5.  Tcvcbtns dnfres — usuglly ogifr, ombfr, emombmsnce fr ngl` emombmsnce mb rfft  pfsmtmfb fr mbvcrsmfb.75   Lmkctm gvfmes tnc tfbgl moplmdgtmfbs f` sudn tcrtmgb strudturcs vmg tnc strgtm`mdgtmfb f` tcxturc8 tnrfukn rnytnomd emssfbgbdc, rcpctmtmvc `mkurgtmfbs, iuxtgpfsmtmfb f` dfbtrgstmbk ngrofbmcs gbe bfb-strudturgl pmtdncs mb nms oclfemd lmbcs.73  7:

 Omkucl G. Qfmk-@rgbdflm, "Ngrofbmd gbe @frogl Zrfdcsscs mb Lmkctm”s Bct-Ttrudturc Dfopfsmtmfbs,"  Ousmd Uncfry Un cfry Tpc Tpcdtruo dtruo  7;, bf. 1 (7==3), nttp9//www.istfr.dfo/stgalc/;53>;4. 77  Tcgray. 71  Kyðrky Lmkctm gbe Zítcr Pçrbgm,  Lmkctm mb Dfbvcrsgtmf D fbvcrsgtmfbb (Ogmbz9 Culcbaurk Affhs, 7=>4).   74  Tcgray. 75  Ttcpncb Gbercw Ugylfr, Unc Lgocbtf Oftm`9 Octgofrpnfsms mb Lmkctm”s Lgtc Ttylc (Bcw ]frh9 Dfrbcll Sbmvcrsmty, 7==5).  73  Crmd Erftt, "Unc Qflc f` Urmgemd Ngrofby mb Lmkctm”s Qcdcbt Ousmd,"  Ousmd Gbglysms G bglysms  11, bf. 4 (1::4), nttps9//www.istfr.frk/stgalc/4;::5406scq?7.

 

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Qnytnomd emssfbgbdc ms cvmecbt mb Lmkctm”s pmgbf wfrh  @gb`grcs, wncrc tnc dfbtrgstmbk rnytnos mb cgdn ngbe drcgtc ngrofbmd goamkumty. Nc plgdcs gb fstmbgtf mb fbc ngbe wnmlc tnc ftncr plgys eyges, gbe gltnfukn cgdn ms dlcgrly aumlt fb trmgemd ngrofby, tncy rcogmb emstmbdt gbe tncmr dfoambce vcrtmdgl ngrofby ubdlcgr. Unms ms euc tf tnc rnytnomd mbecpcbecbdc f` cgdn ngbe, wncrc tnc fstmbgtf rcpcgts tnc sgoc 4+1+4 pgttcrb wnmlc tnc eyges ngvc tncmr fwb rnytno f` 4+1+4+4+1, 4+4+1+4+4 gbe tncb 1+4+4+1+4. Uncsc pgttcrbs kf fut f` pngsc wmtn fbc gbftncr, dgusmbk tncmr dfoambce vcrtmdgl sfbfrmtmcs tf ac dfbstgbtly snm`tmbk wnmdn gvfmes g ubm`mce ngrofbmd ofvcocbt gdrfss tnc pmcdc8 oghmbk usc f` tcrtmgb ngrofby wmtnfut mts `ubdtmfb.70 

7;

@mk. 19 @gb`grcs ogbusdrmpt cxdcrpt.  

Dfrecs ç vmec `cgturcs g ecsdcbembk lmbc f` `m`tns tnrfuknfut tnc pmcdc. Unms lmbc fddurs wmtn sudn rckulgrmty tngt tnc cgr lgtdncs fbtf tnc nfrmzfbtgl bgturc f` mt fvcr mts vcrtmdgl emocbsmfb. [mtn tnc geemtmfb f` lcss prcemdtgalc ogtcrmgl mb tnc ftncr ngbe, tnc rcpctmtmvc `mkurc emombmsncs tnc mopgdt f` tnc vcrtmdgl sfbfrmtmcs `froce actwccb tnc lmbcs gbe oghcs tnco scco lmhc g dfbscqucbdc f` tnc nfrmzfbtgl lmbc rgtncr tngb g ngrofbmd ermvmbk `frdc prfvmembk emrcdtmfb. Unms efombgbdc f` tnc nfrmzfbtgl fvcr tnc vcrtmdgl ergws gttcbtmfb gwgy `rfo tnc

70

 Mame.  Kyðrky Lmkctm - Ítuecs `fr Zmgbf (Affh 7), Bf.5, emrcdtce ay Unfogs Lmkrc, `cgturmbk Meml Amrct (]futuac, 1:74), nttps9//www.yfutuac.d nttps9//www.yfutuac.dfo/wgtdn6v?z fo/wgtdn6v?z[Ig4t`WW3M. [Ig4t`WW3M.

7;

 

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tcrtmgb ngrofbmcs moplmce ay tnc dfoambgtmfb f` aftn ngbes, gbe emlutcs gby ngrofbmd sybtgx 7>  prcscbt.  

7=

@mk. 49 Dfrecs ç vmec ogbusdrmpt cxdcrpt.  

Mb nms pmgbf ctuec Lmkctm drcgtcs g qugsm-tfbglmty ay strgtm`ymbk tnc Yguacrlcnrlmbk, ngrofby actwccb Ecr tnc ngbes. Unc lc`t ngbe ms rcstrmdtce tf tnc algdh-bftc pcbtgtfbmd sdglc wnmlc tnc rmknt ngbe plgys fbly tnc wnmtc hcys. Cgdn ngbe ms rcdfkbmsgaly emgtfbmd, aut tncy dfoambc tf drcgtc g ofrc dnrfogtmd ngrofby fvcrgll. G dfbvcbtmfbgl trmge ms `rcqucbtly `froce wncb tnc ousmdgl `rgkocbts prcscbtce mb cgdn ngbe fvcrlgp, nfwcvcr tnc dfbtrgstmbk tfbglmtmcs f` cgdn pgrt strgtm`mcs tnc tcxturc gbe emskumscs tncsc tcrtmgb sfbfrmtmcs. 1: 

@mk. 59 Gbglysms ay Erftt f` pflytfbglmty gbe cocrkcbt vcrtmdgl sfbfrmtmcs mb  Ecr Yguacrlcnrlmbk. 17 

Unc omeelc scdtmfb f` tnc Gllg Ogrdmg ofvcocbt (ocgsurcs 47-7:4) `rfo Lmkctm”s Nfrb Urmf ms gb cxgoplc f` nfw nms oclfemd wrmtmbk emskumscs tnc prcscbdc f` tcrtmgb sfbfrmtmcs. Erftt gbglyscs Lmkctm”s oclfemd prfdcss gs tnc iuxtgpfsmtmfb f` G gbe A oclfemd gkkrckgtcs, wncrc 7>

 Erftt.   Lmkctm  Lmkctm Ítuecs Ítue cs Zfur Zmgbf, Df Dfrecs recs Ç P Pmec mec, emrcdtce ay Bmdh Qce`crb1:7:), nttps9//www.yfutuac.dfo nttps9//www. yfutuac.dfo/wgtdn6v?`t /wgtdn6v?`tVK>aHmcBd. VK>aHmcBd. 1:  Erftt. 17  Mame. 7=

 

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G ms stgtce twmdc, A twmdc, tncb G gkgmb gbe sf fb. @mk 3  ecpmdts tncsc gkkrckgtcs gbe `mk 0 ms gb cxdcrpt `rfo tnc sncct ousmd. Unc omeelc scdtmfb f` tnc ofvcocbt ms agsce mbmtmglly grfube tncsc oclfemd alfdhs, nfwcvcr Lmkctm mbtrfeudcs geemtmfbgl pmtdncs tfwgres tnc cbe f` tnc scdtmfb. Ackmbbmbk mb agr 3; wmtn tnc nfrb”s D#, tncsc geece tfbcs prfeudc trmges mb dfoambgtmfb wmtn tnc frmkmbgl eyge tcxturc (tnc D# drcgtcs g D# ombfr sfbfrmty), tncb scvcbtn dnfres, bmbtn dnfres, emgtfbmd dlustcrs tncb dnrfogtmd dlustcrs gs ofrc pmtdncs grc geece gdrfss tnc rcst f` tnc scdtmfb. Unms dfbtmbugl geemtmfb f` tfbcs ubecrombcs tnc ngrofbmd tcbecbdy f` tnc frmkmbgl gkkrckgtcs gs tncmr pmtdn mecbtmty ms dlfuece ubecr tnc wcmknt f` bftcs. Unc ngrofbmd agsms f` tnms scdtmfb ms rcdfkbmsgaly tcrtmgb, aut Lmkctm”s usc f` bfbstrudturgl dflfur tfbcs geece tf tnc frmkmbgl pmtdn gkkrckgtcs c``cdtmvcly alcbes tnms tfbglmty wmtn gb gtfbgl goamkumty.11 

@mk. 39 Oclfemd gkkrckgtcs mb tnc Gllg Ogrdmg ofvcocbt f` tnc Nfrb trmf gs gbglysce ay Erftt. 14 

@mk. 09 Cxdcrpt `rfo tnc Gllg Ogrdmg Ofvcocbt f` tnc Nfrb trmf. 15 

Lmkctm”s ngrofbmd lgbkugkc dgb ac suooce up mbtf `fur pcrmfes gdrfss nms ousmdgl futput9 dfbvcbtmfbgl tfbglmty, gtfbgl dlustcr wrmtmbk, gtfbgl omdrfpflypnfbmd-`fdussce dlustcr dfopfsmtmfb gbe qugsm-tfbgl wfrhs.13 Sblmhc Lmkctm”s lgtcr bfb-tfbgl usc f` tcrtmgb strudturcs, M agsce oy pmcdc grfube dfbvcbtmfbgl tfbglmty gbe usce bfb-tfbgl clcocbts `fr geemtmfbgl dflfur. Gspcdts f` nms qugsm-tfbglmty tngt M eme gttcopt tf mbtckrgtc mbtf tnc pmcdc nfwcvcr, wcrc pflytfbglmty gbe geece tfbc sfbfrmtmcs (lmhc nms bfb-strudturgl pmtdncs). M usce

11 14

 Tcgray.  Erftt.

15

 Kyðrky Lmkctm , emrcdtce ay Egofb I.N.H1:7>), - Nfrb Urmf Xwmtn Tdfrc_ nttps9//www. nttps9//www.yfutuac.dfo/ yfutuac.dfo/wgtdn6v?-m wgtdn6v?-m]ytt[k:fs. ]ytt[k:fs. 13  Krm``mtns.

 

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 pflytfbglmty mb tnc ackmbbmbk gbe cbembk scdtmfbs f` oy pmcdc, wncrc M dfoambce tnc ogifr gbe ombfr tfbglmtmcs mb g splmt tnmre dnfre, smomlgr tf Lmkctm”s  Ousmdg Qmdcrdgtg bf. 4. M glsf usce pflytfbglmty gt tnc dlmogx f` tnc wfrh mb ocgsurc 1:, wncrc M coplfyce g pflydnfre dfoprmsmbk f` G ogifr gbe @ ogifr trmges tf aumle tcbsmfb mbtf tnc `fllfwmbk agr. Tmomlgrly tf Lmkctm”s Gllg Ogrdmg ofvcocbt, M usce geece tfbc sfbfrmtmcs `fr `urtncr dflfur gbe tf emskumsc tnc ubecrlymbk tcrtmgb ngrofby (gltnfukn oy pmcdc ms oudn ofrc tfbgl gs g`frcocbtmfbce). Uwf cxgoplcs grc ocgsurcs 1 gbe 3 wncrc M geece ; tn gbe =tn gbe =tn gbe 77tn eckrccs rcspcdtmvcly. Aftn gee tfbgl dflfur mb dfbtrgst tf tnc emssfbgbt splmt tnmre, gbe M  aclmvc tnc agr 3 sfbfrmty c``cdtmvcly alurs tnc trmgemd `fubegtmfb smomlgr tf Lmkctm, cspcdmglly wmtn tnc 77tn mb tnc agss. Uwf gspcdts f` strctdnmbk tfbglmty tngt M lcgrbt ofrc gafut tnrfukn wrmtmbk oy pmcdc wcrc vfmdclcgembk gbe tcbsmfb gbe rclcgsc. Qgtncr tngb tnmbhmbk dfbvcbtmfbglly gafut vfmdclcgembk mb tcros f` sdglc eckrcc gbe dfubtcrpfmbt rulcs, oy alurrmbk f` tnc trmgemd strudturcs ocgbt tngt M wgs `rcc tf vfmdclcge nfw M wgbtce. Mb pgrtmdulgr, M coplfyce mbtcrvgllmd vfmdclcgembk sudn gs tnc lcgembk-tfbc-rclgtce tcbecbdy `fr scomtfbc mbtcrvgls tf wgbt tf rcsflvc (sudn gs mb ocgsurc 7;). M trmce tf sngpc tcbsmfb gbe rclcgsc (qumtc cxgkkcrgtcely) mb cgdn pnrgsc gbe usc g wmec spcdtruo f` emssfbgbt dflfurs, `rfo emgtfbmd suspcbsmfbs tf splmt tnmres gbe tn

gukocbtce ;  dnfres. M glsftfbcs gttcoptce sngpc tnms gt tnrfukn ogbmpulgtmbk wmtn smkbm`mdgbt emvmsm `fr geece (c.k. gttftnc dlmogx ocgsurc 1:) fr ecbscecbsmty, uppcr vfmdmbks tf  aglgbdc tnc tcbsmfb `rfo g ofrc emssfbgbt dnfre tngt prcdcece (sudn gs mb ocgsurc 3). Fvcrgll, M”vc lcgrbt g lft `rfo stueymbk Lmkctm”s ngrofbmd lgbkugkc gbe wrmtmbk oy pmcdc, gbe M lffh `frwgre tf moplcocbtmbk wngt M”vc lcgrbt mb `uturc pmcdcs.

 

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Amalmfkrgpny

Gubcr, Ifscpn. Ousmd mb tnc Uwcbtmctn gbe Uwcbty-@mrst Dcbturmcs Bcw ]frh, Sbmtce Ttgtcs9 [[ Bfrtfb & Df, 1:74. Aurhnflecr, I. Zctcr, Efbgle Igy Krfut, gbe Dlguec v. Zglmsdg.  G Nmstfry f` [cstcrb Ousmd. Cemtce ay Ogrmactn Zgybc. > ce. Lfbefb  Bcw ]frh9 [.[. Bfrtfb & Dfopgby, Dfopgby, Mbd., 1:7:. Erftt, Crmd. "Unc Qflc f` Urmgemd Ngrofby mb Lmkctm”s Qcdcbt Ousmd."  Ousmd Gbglysms 11, bf. 4 (1::4)9 1>4-475. nttps9//www.istfr.frk/stgalc/4;::5406scq?7. nttps9//www.istfr.frk/stgalc/4;::5406scq?7. Krm``mtns, Zgul. Lmkctm, Kyðrky. Krfvc Ousmd Fblmbc9 Fx`fre Sbmvcrsmty Zrcss, 1::7.

 Lmkctm - Gtofspncrcs Emrcdtce ay Kumkuc, Ememcr, 1:71. I .N.H, Egofb, 1:7>. Kyðrky Lmkctm - Nfrb Urmf Xwmtn Tdfrc_ . Emrcdtce ay I.N.H, LMkctm, Kyðrky, G Dgpcllg Gostcrego, Egbmcl Qcuss, gbe Tusgbbc Pgb Cls.  Lmkctm9 Lux  Gctcrbg. no Kfle9 ngrofbmg oubem, 1:70. Lmkctm, Kyðrky gbe Zítcr Pçrbgm. Lmkctm mb Dfbvcrsgtmfb. Ogmbz9 Culcbaurk Affhs, 7=>4.

Kyðrky Lmkctm - Ítuecs `fr Zmgbf (Affh 7), Bf.5. Emrcdtce ay Lmkrc, Unfogs. ]futuac, 1:74. Kyðrky Lmkctm - Ítuecs `fr Zmgbf (Affh 1) Bf. 7:. Emrcdtce ay Lmkrc, Unfogs, 1:73. Ogyvmllc, Ttcpngbmc. "Unc Dfopfsmtmfbgl Ucdnbmqucs gbe Mb`lucbdcs Acnmbe Lmkctm”s „Gtofstpnírcs”." Mbtcroczzf 7 (1:73)9 4:-4>. nttps9//ufttgwg.sdnflgrspfrtgl.mb`f/fttgwg/mbecx.pnp/mbtcroczzf/grtmdlc/vmcw/74>5. Zgslcr, Igbb. Zfstofecrbmso. Krfvc Ousmd Fblmbc9 Fx`fre Sbmvcrsmty Zrcss, 1::7. Zcrsmdncttm, Pmbdcbt. Uwcbtmctn-Dcbtury Ngrofby9 Drcgtmvc Gspcdts gbe Zrgdtmdc . Mllustrgtce Cemtmfb ce. Bcw ]frh9 [.[. Bfrtfb & Df. Mbd., 7=07.

 Lmkctm Ítuecs Zfur Zmgbf, Dfrecs Ç Pmec Pmec. Emrcdtce ay Qce`crb, Bmdh, 1:7:. Qfmk-@rgbdflm, Omkucl G. "Ngrofbmd gbe @frogl Zrfdcsscs mb Lmkctm”s Bct-Ttrudturc Dfopfsmtmfbs." Ousmd Uncfry Tpcdtruo 7;, bf. 1 (7==3)9 151-0;. nttp9//www.istfr.dfo/stgalc/;53>;4.. nttp9//www.istfr.dfo/stgalc/;53>;4 Tcgray, Omhc. "Lmkctm tnc Zfstofecrbmst6" Ucopf, bf. 7== (7==;)9 =-75. nttps9//www.istfr.frk/stgalc/=533136scq?7 nttps9//www.istfr.frk/stgalc/=533136scq?7.. Ugylfr, Ttcpncb Gbercw. Unc Lgocbtf Oftm`9 Octgofrpnfsms mb Lmkctm”s Lgtc Ttylc . Bcw ]frh9 Dfrbcll Sbmvcrsmty, 7==5.

 

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